Question: Simplify. Rewrite the expression in the form $7^n$. $\left(7^3\right)^{3}=$
$\begin{aligned} \left(7^3\right)^{3}&=7^{3\cdot 3} \\\\ &=7^{9} \end{aligned}$ This follows from the general rule $\left(x^m\right)^{n}=x^{m\cdot n}$. We can also see this is correct by expanding the powers. $\begin{aligned} \left(7^3\right)^{3}&=\underbrace{7^3\cdot 7^3\cdot 7^3}_\text{3 times} \\\\\\ &=\underbrace{ \underbrace{7\cdot 7\cdot 7}_\text{3 times} \cdot \underbrace{7\cdot 7\cdot 7}_\text{3 times} \cdot \underbrace{7\cdot 7\cdot 7}_\text{3 times}} _\text{3 times} \\\\ &=7^{9} \end{aligned}$ In conclusion, $\left(7^3\right)^{3}=7^{9}$.